Basic Geometrical Concepts (Exercise 10.1) RD Sharma Solutions | Mathematics (Maths) Class 6 PDF Download

 Page 1


 
 
 
 
 
 
Exercise 10.1                                                                             page: 10.7 
1. Make three points in your notebook and name them. 
Solution: 
 
The three points A, P and H are marked as given below: 
 
 
2. Draw a line in your notebook and name it using a small letter of the alphabet. 
Solution: 
 
The line AB is drawn and is named as l 
 
 
3. Draw a line in your notebook and name it by taking any two points on it. 
Solution: 
 
Construct a line and name the points PQ. It can be called as the line PQ. 
 
 
4. Give three examples from your environment of: 
(i) Points 
(ii) Portion of a line 
(iii) Plane surfaces 
(iv) Portion of a plane 
(v) Curved surfaces 
Solution: 
 
(i) Points  
The three examples are 
Pinhole on the map 
Two walls and floor meeting at the corner 
Period at the end of the sentence 
 
(ii) Portion of a line 
Page 2


 
 
 
 
 
 
Exercise 10.1                                                                             page: 10.7 
1. Make three points in your notebook and name them. 
Solution: 
 
The three points A, P and H are marked as given below: 
 
 
2. Draw a line in your notebook and name it using a small letter of the alphabet. 
Solution: 
 
The line AB is drawn and is named as l 
 
 
3. Draw a line in your notebook and name it by taking any two points on it. 
Solution: 
 
Construct a line and name the points PQ. It can be called as the line PQ. 
 
 
4. Give three examples from your environment of: 
(i) Points 
(ii) Portion of a line 
(iii) Plane surfaces 
(iv) Portion of a plane 
(v) Curved surfaces 
Solution: 
 
(i) Points  
The three examples are 
Pinhole on the map 
Two walls and floor meeting at the corner 
Period at the end of the sentence 
 
(ii) Portion of a line 
 
 
 
 
 
 
The three examples are 
Thin curtain rods 
Laser beams 
Stretched power cables 
 
(iii) Plane surfaces 
The three examples are 
Surface of a white board 
Top of a table 
Surface of a wall 
 
(iv) Portion of a plane 
The three examples are 
Surface of a mirror 
Calm water in a swimming pool 
Surface of the sheet of paper 
 
(v) Curved surfaces 
The three examples are 
Ink pot 
Tea pot 
Gas cylinder 
 
5. There are a number of ways by which we can visualise a portion of a line. State whether the following 
represent a portion of a line or not: 
(i) A piece of elastic stretched to the breaking point. 
(ii) Wire between two electric poles. 
(iii) The line thread by which a spider lowers itself. 
Solution: 
 
(i) Yes.  
 
(ii) No.  
 
(iii) Yes.  
 
6. Can you draw a line on the surface of a sphere which lies wholly on it? 
Solution: 
 
No. A line cannot be drawn on the surface of the sphere which lies wholly on it. 
 
7. Mark a point on a sheet of paper and draw a line passing through it. How many lines can you draw 
through this point? 
Solution: 
 
Unlimited number of lines can be drawn through the point L. 
Page 3


 
 
 
 
 
 
Exercise 10.1                                                                             page: 10.7 
1. Make three points in your notebook and name them. 
Solution: 
 
The three points A, P and H are marked as given below: 
 
 
2. Draw a line in your notebook and name it using a small letter of the alphabet. 
Solution: 
 
The line AB is drawn and is named as l 
 
 
3. Draw a line in your notebook and name it by taking any two points on it. 
Solution: 
 
Construct a line and name the points PQ. It can be called as the line PQ. 
 
 
4. Give three examples from your environment of: 
(i) Points 
(ii) Portion of a line 
(iii) Plane surfaces 
(iv) Portion of a plane 
(v) Curved surfaces 
Solution: 
 
(i) Points  
The three examples are 
Pinhole on the map 
Two walls and floor meeting at the corner 
Period at the end of the sentence 
 
(ii) Portion of a line 
 
 
 
 
 
 
The three examples are 
Thin curtain rods 
Laser beams 
Stretched power cables 
 
(iii) Plane surfaces 
The three examples are 
Surface of a white board 
Top of a table 
Surface of a wall 
 
(iv) Portion of a plane 
The three examples are 
Surface of a mirror 
Calm water in a swimming pool 
Surface of the sheet of paper 
 
(v) Curved surfaces 
The three examples are 
Ink pot 
Tea pot 
Gas cylinder 
 
5. There are a number of ways by which we can visualise a portion of a line. State whether the following 
represent a portion of a line or not: 
(i) A piece of elastic stretched to the breaking point. 
(ii) Wire between two electric poles. 
(iii) The line thread by which a spider lowers itself. 
Solution: 
 
(i) Yes.  
 
(ii) No.  
 
(iii) Yes.  
 
6. Can you draw a line on the surface of a sphere which lies wholly on it? 
Solution: 
 
No. A line cannot be drawn on the surface of the sphere which lies wholly on it. 
 
7. Mark a point on a sheet of paper and draw a line passing through it. How many lines can you draw 
through this point? 
Solution: 
 
Unlimited number of lines can be drawn through the point L. 
 
 
 
 
 
 
 
 
8. Mark any two points P and Q in your note book and draw a line passing through the points. How many 
lines can you draw passing through both the points? 
Solution: 
 
Draw a line passing through the points P and Q 
Only one line can be drawn passing through this both points. 
 
 
9. Give an example of a horizontal plane and a vertical plane from your environment. 
Solution: 
 
The example of horizontal plane is ceiling of a room. 
The example of a vertical plane is wall of a room.  
 
10. How many lines may pass through one given point, two given points, any three collinear points? 
Solution: 
 
The lines passing through one given point is unlimited. 
 
The lines passing through two given points are only one. 
Page 4


 
 
 
 
 
 
Exercise 10.1                                                                             page: 10.7 
1. Make three points in your notebook and name them. 
Solution: 
 
The three points A, P and H are marked as given below: 
 
 
2. Draw a line in your notebook and name it using a small letter of the alphabet. 
Solution: 
 
The line AB is drawn and is named as l 
 
 
3. Draw a line in your notebook and name it by taking any two points on it. 
Solution: 
 
Construct a line and name the points PQ. It can be called as the line PQ. 
 
 
4. Give three examples from your environment of: 
(i) Points 
(ii) Portion of a line 
(iii) Plane surfaces 
(iv) Portion of a plane 
(v) Curved surfaces 
Solution: 
 
(i) Points  
The three examples are 
Pinhole on the map 
Two walls and floor meeting at the corner 
Period at the end of the sentence 
 
(ii) Portion of a line 
 
 
 
 
 
 
The three examples are 
Thin curtain rods 
Laser beams 
Stretched power cables 
 
(iii) Plane surfaces 
The three examples are 
Surface of a white board 
Top of a table 
Surface of a wall 
 
(iv) Portion of a plane 
The three examples are 
Surface of a mirror 
Calm water in a swimming pool 
Surface of the sheet of paper 
 
(v) Curved surfaces 
The three examples are 
Ink pot 
Tea pot 
Gas cylinder 
 
5. There are a number of ways by which we can visualise a portion of a line. State whether the following 
represent a portion of a line or not: 
(i) A piece of elastic stretched to the breaking point. 
(ii) Wire between two electric poles. 
(iii) The line thread by which a spider lowers itself. 
Solution: 
 
(i) Yes.  
 
(ii) No.  
 
(iii) Yes.  
 
6. Can you draw a line on the surface of a sphere which lies wholly on it? 
Solution: 
 
No. A line cannot be drawn on the surface of the sphere which lies wholly on it. 
 
7. Mark a point on a sheet of paper and draw a line passing through it. How many lines can you draw 
through this point? 
Solution: 
 
Unlimited number of lines can be drawn through the point L. 
 
 
 
 
 
 
 
 
8. Mark any two points P and Q in your note book and draw a line passing through the points. How many 
lines can you draw passing through both the points? 
Solution: 
 
Draw a line passing through the points P and Q 
Only one line can be drawn passing through this both points. 
 
 
9. Give an example of a horizontal plane and a vertical plane from your environment. 
Solution: 
 
The example of horizontal plane is ceiling of a room. 
The example of a vertical plane is wall of a room.  
 
10. How many lines may pass through one given point, two given points, any three collinear points? 
Solution: 
 
The lines passing through one given point is unlimited. 
 
The lines passing through two given points are only one. 
 
 
 
 
 
 
 
The lines passing through three collinear points are one. 
 
 
11. Is it ever possible for exactly one line to pass through three points? 
Solution: 
 
Yes. It is possible for a line to pass through three points, if the points lie on a straight line. 
 
 
12. Explain why it is not possible for a line to have a mid-point. 
Solution: 
 
We know that the length of the line is infinite and it is not possible to find the midpoint. 
But it is possible to find the midpoint of line segments. 
 
13. Mark three non-collinear points A, B and C in your note book. Draw lines through these points taking 
two at a time. Name these lines. How many such different lines can be drawn? 
Solution: 
 
It is given that the three collinear points are A, B and C 
We know that three lines namely AB, BC and AC can be drawn using these points. 
Page 5


 
 
 
 
 
 
Exercise 10.1                                                                             page: 10.7 
1. Make three points in your notebook and name them. 
Solution: 
 
The three points A, P and H are marked as given below: 
 
 
2. Draw a line in your notebook and name it using a small letter of the alphabet. 
Solution: 
 
The line AB is drawn and is named as l 
 
 
3. Draw a line in your notebook and name it by taking any two points on it. 
Solution: 
 
Construct a line and name the points PQ. It can be called as the line PQ. 
 
 
4. Give three examples from your environment of: 
(i) Points 
(ii) Portion of a line 
(iii) Plane surfaces 
(iv) Portion of a plane 
(v) Curved surfaces 
Solution: 
 
(i) Points  
The three examples are 
Pinhole on the map 
Two walls and floor meeting at the corner 
Period at the end of the sentence 
 
(ii) Portion of a line 
 
 
 
 
 
 
The three examples are 
Thin curtain rods 
Laser beams 
Stretched power cables 
 
(iii) Plane surfaces 
The three examples are 
Surface of a white board 
Top of a table 
Surface of a wall 
 
(iv) Portion of a plane 
The three examples are 
Surface of a mirror 
Calm water in a swimming pool 
Surface of the sheet of paper 
 
(v) Curved surfaces 
The three examples are 
Ink pot 
Tea pot 
Gas cylinder 
 
5. There are a number of ways by which we can visualise a portion of a line. State whether the following 
represent a portion of a line or not: 
(i) A piece of elastic stretched to the breaking point. 
(ii) Wire between two electric poles. 
(iii) The line thread by which a spider lowers itself. 
Solution: 
 
(i) Yes.  
 
(ii) No.  
 
(iii) Yes.  
 
6. Can you draw a line on the surface of a sphere which lies wholly on it? 
Solution: 
 
No. A line cannot be drawn on the surface of the sphere which lies wholly on it. 
 
7. Mark a point on a sheet of paper and draw a line passing through it. How many lines can you draw 
through this point? 
Solution: 
 
Unlimited number of lines can be drawn through the point L. 
 
 
 
 
 
 
 
 
8. Mark any two points P and Q in your note book and draw a line passing through the points. How many 
lines can you draw passing through both the points? 
Solution: 
 
Draw a line passing through the points P and Q 
Only one line can be drawn passing through this both points. 
 
 
9. Give an example of a horizontal plane and a vertical plane from your environment. 
Solution: 
 
The example of horizontal plane is ceiling of a room. 
The example of a vertical plane is wall of a room.  
 
10. How many lines may pass through one given point, two given points, any three collinear points? 
Solution: 
 
The lines passing through one given point is unlimited. 
 
The lines passing through two given points are only one. 
 
 
 
 
 
 
 
The lines passing through three collinear points are one. 
 
 
11. Is it ever possible for exactly one line to pass through three points? 
Solution: 
 
Yes. It is possible for a line to pass through three points, if the points lie on a straight line. 
 
 
12. Explain why it is not possible for a line to have a mid-point. 
Solution: 
 
We know that the length of the line is infinite and it is not possible to find the midpoint. 
But it is possible to find the midpoint of line segments. 
 
13. Mark three non-collinear points A, B and C in your note book. Draw lines through these points taking 
two at a time. Name these lines. How many such different lines can be drawn? 
Solution: 
 
It is given that the three collinear points are A, B and C 
We know that three lines namely AB, BC and AC can be drawn using these points. 
 
 
 
 
 
 
 
 
14. Coplanar points are the points that are in the same plane. Thus, 
(i) Can 150 points be coplanar? 
(ii) Can 3 points be non-coplanar? 
Solution: 
 
(i) Yes. We know that the group of points which lie in the same plane are coplanar points. 
Hence, 150 points can be coplanar. 
 
(ii) No. We know that 3 points can be coplanar as we can have plane which contains 3 points. 
Hence, 3 points cannot be non-coplanar. 
 
15. Using a ruler, check whether the following points given in Fig. 10.30 are collinear or not: 
(i) D, A and C 
(ii) A, B and C 
(iii) A, B and E 
(iv) B, C and E 
 
Solution: 
 
(i) The points D, A and C are collinear. 
 
(ii) The points A, B and C are non-collinear. 
 
(iii) The points A, B and E are collinear. 
 
(iv) The points B, C and E are non-collinear. 
 
16. Lines p, q are coplanar. So are the lines p, r. Can we conclude that the lines p, q, r are coplanar? 
Solution: